Die navorsing is onderneem om die invloed van koöperatiewe leer as „n onderrigstrategie op Graad 8 wiskundeleerders se houding teenoor probleemoplossing en hul prestasie in wiskunde te bepaal. Die doelstellings van die empiriese ondersoek was: - om die houding van Graad 8 leerders teenoor wiskunde en teenoor probleemoplossing in wiskunde te ondersoek; - om die invloed van koöperatiewe leer as onderrigstrategie op die houding van graad 8 wiskunde-leerders teenoor wiskunde en teenoor probleemoplossing in wiskunde te ondersoek; en - om die invloed van koöperatiewe leer as onderrigstrategie op die prestasie van Graad 8 leerders in wiskunde te ondersoek. Deur middel van „n literatuurstudie as onderrig-leerraamwerk, is die aard van skoolwiskunde; benaderings ten opsigte van die leer van skoolwiskunde, naamlik die behavioristiese-, die kognitiewe- en die konstruktiwistiese leerbenaderings; die rol van probleemoplossing in die onderrig en leer van skoolwiskunde; asook die houding van leerders teenoor wiskunde en teenoor probleemoplossing in wiskunde, bespreek. Na aanleiding van die gebruik van direkte- en indirekte onderrigstrategieë, is die volgende elemente van koöperatiewe leer (indirekte onderrigstrategie) beklemtoon: individuele verantwoordelikheid, interpersoonlike sosiale vaardighede, positiewe persoonlike interaksie, groepvordering en positiewe interafhanklikheid. Koöperatiewe leermetodes en die implementering van koöperatiewe leer in die wiskundeklaskamer is vervolgens bespreek, asook leerders se houding teenoor koöperatiewe leer. Vir die empiriese ondersoek is „n opeenvolgende verklarende gekombineerde navorsingsmetode-ontwerp gebruik, wat bestaan het uit die insameling en ontleding van kwantitatiewe- en kwalitatiewe data in opeenvolgende fases. „n Voor-eksperimentele evaluering (voortoets) is gedoen om die eksperimentele en kontrolegroepe te vergelyk ten opsigte van hul houding teenoor wiskunde en teenoor probleemoplossing in wiskunde deur die gebruik van „n aangepaste houdingsvraelys (ATMI), asook ten opsigte van leerders se wiskundeprestasie. Die intervensie (koöperatiewe leer as onderrigstrategie) is vervolgens vir „n tydperk van sestien weke op die eksperimentele groep toegepas. Die aangepaste houdingsvraelys (ATMI) is ook tydens „n na-eksperimentele evaluering (natoets) vir beide (kontrole- en eksperimentele) groepe gebruik, asook vir die vergelyking van genoemde groepe se wiskundeprestasie. Die kwalitatiewe ondersoek is uitgevoer deur individuele gestruktureerde taakgebaseerde onderhoude met geselekteerde deelnemers van die eksperimentele groep te voer. Inligting oor leerders se houding en ervaring ten opsigte van probleemoplossing in wiskunde, hul houding teenoor koöperatiewe leer, asook hul probleemoplossingsvaardighede, is met behulp van die onderhoude bekom. Uit die resultate van die empiriese navorsing is bevind dat koöperatiewe leer as onderrigstrategie geen beduidende invloed op Graad 8 leerders se houding teenoor wiskunde en teenoor probleemoplossing in wiskunde gehad het nie. Die gebruik van koöperatiewe leer as onderrigstrategie daarenteen, het „n beduidende toename in Graad 8 leerders se prestasie in wiskunde tot gevolg gehad. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2015

Mainz, Universiẗat, Diss. : 1995.

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

As a result of the interactive nature of modern programming languages the perception has developed that proper planning of a solution, reasoned action during the process of problem solving and evaluation of the solution have become less important during computer programming. Learn often rely on the programming language to help them solve a problem, without themselves planning the solution beforehand and then using a computer language to implement the solution. This approach usually leads to using bad programming techniques, resulting in unstructured programmes or rendering the learner unable to solve the problem. The importance of continuous reflection by learners while doing a programming activity has been advocated for quite some time... / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

As a result of the interactive nature of modern programming languages the perception has developed that proper planning of a solution, reasoned action during the process of problem solving and evaluation of the solution have become less important during computer programming. Learn often rely on the programming language to help them solve a problem, without themselves planning the solution beforehand and then using a computer language to implement the solution. This approach usually leads to using bad programming techniques, resulting in unstructured programmes or rendering the learner unable to solve the problem. The importance of continuous reflection by learners while doing a programming activity has been advocated for quite some time... / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

The purpose of this study is to focus on constructing a modelling-based learning environment to improve learner performance in grade 6 mathematics classrooms. The purpose emanates from the continued poor performance of learners in mathematics at different school levels, especially grade 6. The teaching and learning of mathematics is explained from an ontological point of departure, focussing on constructivist paradigms. Different types of constructivism are discussed with special attention to the school mathematics domain. The learning, problem based learning, problem solving and learning environment are key components in the discussion. A theoretical perspective on the design of modelling as a powerful learning environment in primary schools mathematics classrooms is provided. Focus is placed on the applicability of the modelling-based learning environment on the South African mathematics curriculum and on study orientation as a key component to help develop an understanding of why learners perform or do not perform in mathematics. A mixed method research design, in which quantitative and qualitative are combined to achieve the outcomes of the research problem, is chosen for this research study project to provide a purposeful research framework. The findings of the research include not only learners’ improvement in dealing with non-routine, mathematical word problems but also in general-routine, mathematical word problems. A second finding shows that the overall SOM pre/post/retention showed good reliability, acceptable construct validity, good practical significance, and large effect but had low to medium effect in individual fields. The univariate analysis for the Crossover design used indicated that the problem solving field had statistical significance and practical significance, and the study milieu and mathematical confidence field might have statistical significance and practical significance. The third finding provided evidence concerning teacher administration, teacher and learner interaction, assessment and homework. The findings from the quantitative and qualitative data-analysis and interpretations, and literature review, guided the researcher in proposing a construct for a modelling-based learning environment as a means to improve learners’ mathematics performance in grade 6 mathematics classes in the John Toalo Gaetswe (JTG) District. The contribution that this study makes is to propose a construct for a modelling-based learning environment to improve learner performance in grade 6 mathematics. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

The purpose of this study is to focus on constructing a modelling-based learning environment to improve learner performance in grade 6 mathematics classrooms. The purpose emanates from the continued poor performance of learners in mathematics at different school levels, especially grade 6. The teaching and learning of mathematics is explained from an ontological point of departure, focussing on constructivist paradigms. Different types of constructivism are discussed with special attention to the school mathematics domain. The learning, problem based learning, problem solving and learning environment are key components in the discussion. A theoretical perspective on the design of modelling as a powerful learning environment in primary schools mathematics classrooms is provided. Focus is placed on the applicability of the modelling-based learning environment on the South African mathematics curriculum and on study orientation as a key component to help develop an understanding of why learners perform or do not perform in mathematics. A mixed method research design, in which quantitative and qualitative are combined to achieve the outcomes of the research problem, is chosen for this research study project to provide a purposeful research framework. The findings of the research include not only learners’ improvement in dealing with non-routine, mathematical word problems but also in general-routine, mathematical word problems. A second finding shows that the overall SOM pre/post/retention showed good reliability, acceptable construct validity, good practical significance, and large effect but had low to medium effect in individual fields. The univariate analysis for the Crossover design used indicated that the problem solving field had statistical significance and practical significance, and the study milieu and mathematical confidence field might have statistical significance and practical significance. The third finding provided evidence concerning teacher administration, teacher and learner interaction, assessment and homework. The findings from the quantitative and qualitative data-analysis and interpretations, and literature review, guided the researcher in proposing a construct for a modelling-based learning environment as a means to improve learners’ mathematics performance in grade 6 mathematics classes in the John Toalo Gaetswe (JTG) District. The contribution that this study makes is to propose a construct for a modelling-based learning environment to improve learner performance in grade 6 mathematics. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

The South African context, in particular, is characterized by a definite need for the facilitation of the development of the youth in a more positive trajectory. Family structures are not always robust enough to support the positive development of the youth, owing to the demands made on single–parent families, amongst other reasons. Community structures may also be less supportive of the development of the youth, because of the impact of the changes associated with the transitional phase of the country during the past sixteen years (Meehan, Peirson & Fridjhon, 2007). Furthermore, young people under the age of 15 years comprise almost a third of the total South African population (Statistics South Africa, 2009), and in the future, they will have to be prepared for an adulthood faced with previously unknown challenges (United Nations Population Fund). The importance of the development of the youth, in order to enable them to contribute to their country in future, is acknowledged by the South African Governement (National Youth Commission website). This study was conducted within the parameters of the newly developing positive youth development (PYD) paradigm. The empirical level of this paradigm is well represented in the literature, indicating that the content areas, or the “what” of PYD, have been well elucidated. However, there is a lack of theory, especially with regard to models describing developmental change (Larson et al., 2004), and evaluation of interventions aiming at the facilitation of PYD. In order to contribute to the answering of the questions regarding the “how” of development, this study had the following main aims: a) the compilation of a theoretical model, describing developmental change in the youth; b) the operationalization of this model for intervention purposes; and c) the evaluation of a programme and the model on which it is based. The study is reported on in an article format, and comprises a total of three articles. The first article focuses on the process of the compilation of a theoretical model by means of: a) the construction of a comprehensive meta–theoretical matrix, b) the integration of theory that features in the PYD literature, and c) the expansion of the latter with theory from other compatible sub–disciplines in psychology. The resultant Positive Youth Development Intervention (PYDI) model provides a process–related description of developmental change ? and is one of the first models to do so. The second article describes the operationalization of the PYDI model, by means of an indication of the relevant constructs, phenomena and processes to be facilitated. Although recent research points to a relation between PYD and self–regulation, there has been no model, describing the role of self–regulation in the facilitation of the positive development of the youth. This study adapted a model from an educational context (Heckhausen & Gollwitzer, 1987 (as cited in Boekaerts & Niemivirta, 2005)), in order to describe the regular self–regulatory processes constituting the bi–directional interactions between the youth and their primary life contexts, as proposed by developmental systems theory (Lerner, 1998), the meta–theory to PYD (King et al., 2005). A further specifc contribution is that the presentation aspects of the programme material, aimed at facilitating the integration thereof, are addressed on a theoretical level. The third article describes the evaluation of the PYDI model and programme, with young adolescents in a school in a rural area as participants. A mixed–methods study, which has been shown to render much richer information than a quantitative study alone, was applied. Although the quantitative data did not prove the success of the programme, the qualitative data suggested that some aspects of self–regulation had indeed been facilitated successfully. A second follow–up assessment, conducted seventeen months later, indicated that certain skills had only become internalized by that time, suggesting that the implementation and evaluation of such a programme should be expanded over an extended time–frame. This study has contributed to the level of theory of PYD, by indicating, a) the lacunae, and b) that theory in compatible sub–disciplinary paradigms could be used in order to devise workable models for PYD. Furthermore, the process–related nature of the PYDI model and programme, owing to its adaptability to different needs, may be adapted and extended to be applicable to the needs of the diverse South African population. Recommendations regarding future application and research, especially within the South African context, have also been put forward in the study. / Thesis (Ph.D. (Psychology))--North-West University, Potchefstroom Campus, 2011.

The South African context, in particular, is characterized by a definite need for the facilitation of the development of the youth in a more positive trajectory. Family structures are not always robust enough to support the positive development of the youth, owing to the demands made on single–parent families, amongst other reasons. Community structures may also be less supportive of the development of the youth, because of the impact of the changes associated with the transitional phase of the country during the past sixteen years (Meehan, Peirson & Fridjhon, 2007). Furthermore, young people under the age of 15 years comprise almost a third of the total South African population (Statistics South Africa, 2009), and in the future, they will have to be prepared for an adulthood faced with previously unknown challenges (United Nations Population Fund). The importance of the development of the youth, in order to enable them to contribute to their country in future, is acknowledged by the South African Governement (National Youth Commission website). This study was conducted within the parameters of the newly developing positive youth development (PYD) paradigm. The empirical level of this paradigm is well represented in the literature, indicating that the content areas, or the “what” of PYD, have been well elucidated. However, there is a lack of theory, especially with regard to models describing developmental change (Larson et al., 2004), and evaluation of interventions aiming at the facilitation of PYD. In order to contribute to the answering of the questions regarding the “how” of development, this study had the following main aims: a) the compilation of a theoretical model, describing developmental change in the youth; b) the operationalization of this model for intervention purposes; and c) the evaluation of a programme and the model on which it is based. The study is reported on in an article format, and comprises a total of three articles. The first article focuses on the process of the compilation of a theoretical model by means of: a) the construction of a comprehensive meta–theoretical matrix, b) the integration of theory that features in the PYD literature, and c) the expansion of the latter with theory from other compatible sub–disciplines in psychology. The resultant Positive Youth Development Intervention (PYDI) model provides a process–related description of developmental change ? and is one of the first models to do so. The second article describes the operationalization of the PYDI model, by means of an indication of the relevant constructs, phenomena and processes to be facilitated. Although recent research points to a relation between PYD and self–regulation, there has been no model, describing the role of self–regulation in the facilitation of the positive development of the youth. This study adapted a model from an educational context (Heckhausen & Gollwitzer, 1987 (as cited in Boekaerts & Niemivirta, 2005)), in order to describe the regular self–regulatory processes constituting the bi–directional interactions between the youth and their primary life contexts, as proposed by developmental systems theory (Lerner, 1998), the meta–theory to PYD (King et al., 2005). A further specifc contribution is that the presentation aspects of the programme material, aimed at facilitating the integration thereof, are addressed on a theoretical level. The third article describes the evaluation of the PYDI model and programme, with young adolescents in a school in a rural area as participants. A mixed–methods study, which has been shown to render much richer information than a quantitative study alone, was applied. Although the quantitative data did not prove the success of the programme, the qualitative data suggested that some aspects of self–regulation had indeed been facilitated successfully. A second follow–up assessment, conducted seventeen months later, indicated that certain skills had only become internalized by that time, suggesting that the implementation and evaluation of such a programme should be expanded over an extended time–frame. This study has contributed to the level of theory of PYD, by indicating, a) the lacunae, and b) that theory in compatible sub–disciplinary paradigms could be used in order to devise workable models for PYD. Furthermore, the process–related nature of the PYDI model and programme, owing to its adaptability to different needs, may be adapted and extended to be applicable to the needs of the diverse South African population. Recommendations regarding future application and research, especially within the South African context, have also been put forward in the study. / Thesis (Ph.D. (Psychology))--North-West University, Potchefstroom Campus, 2011.